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Math 2414 Calculus II Information

LSC-CyFair Math Department

Catalog Description
Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of the definite integral, the calculus of transcendental functions, parametric equations, polar coordinates, indeterminate forms and L’Hopital’s Rule, improper integrals, sequences and series.
Course Learning Outcomes
The student will:
• Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
• Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
• Define an improper integral.
• Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
• Determine convergence or divergence of sequences and series.
• Use Taylor and MacLaurin series to represent functions.
• Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
• Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections.
• Apply L'hôpital's Rule to evaluate limits of indeterminate forms.
Contact Hour Information
Credit Hours:  4
Lecture Hours:  3
Lab Hours:  2
External Hours:  0
Total Contact Hours:  80
Prerequisites
MATH 2413;
ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing
Corequisite
ENGL 0307


Required Materials

Textbook:
William Briggs, Lyle Cochran, Bernard Gillett; Calculus for Scientists and Engineers, Early Transcendentals; Pearson, 2013, ISBN Numbers:
          Textbook Plus Maple Software and MyMathLab Portal Access:  9781269374965
          Textbook Only:  9780321785374
          MyMathLab Portal Access Only:  9780558357603

Calculator:
Graphing Calculator required.  TI 83, TI 84 or TI 86 series calculators recommended. 
Calculators capable of symbolic manipulation will not be allowed on tests.  Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models. 
Neither cell phones nor PDA’s can be used as calculators.  Calculators may be cleared before tests.

Differentiation and Integration Formulas:
Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.

Textbook Sections (for Fall, 2013 only)

Preliminaries

3.8  Derivatives of Logarithmic and Exponential Functions 

3.9  Derivatives of Inverse Trigonometric Functions

4.7  L'Hopital's Rule

6.8  Logarithmic and Exponential Functions Revisited

6.9  Exponential Models

6.10  Hyperbolic Functions
 

Chapter 7.  Integration Techniques

7.1  Basic Approaches

7.2  Integration by Parts

7.3  Trigonometric Integrals

7.4  Trigonometric Substitution

7.5  Partial Fractions

7.6  Other Integration Strategies

7.7  Numerical Integration

7.8  Improper Integrals
 

Chapter 8.  Differential Equations

8.1  Basic Ideas

8.3  Separable Differential Equations


Chapter 9.  Sequences and Infinite Series

9.1  An Overview

9.2  Sequences

9.3  Infinite Series

9.4  The Divergence and Integral Tests

9.5  The Ratio, Root and Comparison Tests

9.6  Alternating Series
 

Chapter 10.  Power Series

10.1  Approximating Functions with Polynomials

10.2  Properties of Power Series

10.3  Taylor Series

10.4  Working with Taylor Series


Chapter 11.  Parametric and Polar Curves

11.1  Parametric Equations

11.2  Polar Coordinates

11.3  Calculus in Polar Coordinates

11.4  Conic Sections


Textbook Sections (Effective Spring, 2014)


Chapter 6.  Appliations of Integration

6.1  Velocity and Net Change

6.2  Regions Between Curves

6.3  Volume by Slicing

6.4  Volume by Shells

6.5  Lengths of Curves

6.6  Surface Area

6.7  Physical Applications (cover work and density and mass; all other topics optional)

6.8  Logarithmic and Exponential Functions Revisited

6.9  Exponential Models

6.10  Hyperbolic Functions

Chapter 7.  Integration Techniques

7.1  Basic Approaches

7.2  Integration by Parts

7.3  Trigonometric Integrals

7.4  Trigonometric Substitution

7.5  Partial Fractions

7.6  Other Integration Strategies

7.7  Numerical Integration

7.8  Improper Integrals
 

Chapter 8.  Differential Equations

8.1  Basic Ideas

8.3  Separable Differential Equations


Chapter 9.  Sequences and Infinite Series

9.1  An Overview

9.2  Sequences

9.3  Infinite Series

9.4  The Divergence and Integral Tests

9.5  The Ratio, Root and Comparison Tests

9.6  Alternating Series
 

Chapter 10.  Power Series

10.1  Approximating Functions with Polynomials

10.2  Properties of Power Series

10.3  Taylor Series

10.4  Working with Taylor Series


Chapter 11.  Parametric and Polar Curves

11.1  Parametric Equations

11.2  Polar Coordinates

11.3  Calculus in Polar Coordinates

11.4  Conic Sections

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